Is it possible to make a change that affects the whole animation but keeps the original animation relative to the change? (like 3ds Max)
Let's start with a simple animation.

With the Delta Transforms
I think this would be the preferred way to do it since it is pretty straightforward.
Head in to the object properties and expand the Delta Transforms panel. There you can add an additional transform that will be added to the animation.

Note the Delta Transforms can also be animated.
With the graph editor :
Hide all the channel you want don't want to offset. Select the channels you want to offset with A while hovering over the curves.

Now type G, Y, 100 and Enter to validate. This will grab (G) the curves, and move them uniformly along the Y axis (the actual transforms values) by 100 units.
Note that if you press G, X and a value this will offset the keyframes along the time axis.
You can also access the Grab tool by going Key &gt; Transform &gt; Move